The word you are looking for is "oxidizer" (because oxygen per se is not required), and space craft carry their own along with their fuel. Often they carry liquid-oxygen as their oxidizer, though I believe other substances have been tried.
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dmckee♦Dec 1 '11 at 16:44

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The Sun isn't "made of fire". It's made mostly of hydrogen and helium. Its heat and light come from nuclear fusion, a very different process that doesn't require oxygen. Ordinary fire is a chemical reaction; fusion merges hydrogen nuclei into helium, and produces much more energy. (Other nuclear reactions are possible.)

As for rockets, they carry both fuel and oxygen (or another oxidizer) with them (at least chemical rockets do; there are other kinds). That's the difference between a rocket engine and a jet engine; jets carry fuel, but get oxygen from the air.

Not all rockets require oxidizer. Nuclear thermal rockets use the energy from a nuclear reactor in place of chemical energy to heat the fuel and generate thrust. Solar thermal rockets have also been proposed.
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Patrick RitchieDec 7 '11 at 15:01